The question there is how people would react to having their tickets checked again and again every time they re-enter a stand.
If you are a season ticket holder, you probably carry it, if like me you pay on the day, once inside I've been know to bin it, or lose it.
What if a family go and like mine the chief holds all the season tickets, it's the whole issue of challenging people and what happens if they can't prove.
It's best to have a simple rule as discretionary rules where some stewards would be by the book others less so would lead to problems.
Closing the gates is the only realistic option, unless you were going to turnstyle the stands themselves, but that would be
a) expensive
b) a true H&S nightmare if a quick evac was needed.
No other modern sporting venues allow un governed movement between stands and whilst it was a noble idea, in the end those who decided to move spoiled that dead.
But I am surprised you can get between south and West. I wonder if that's because of the family stand area.